Any physics gurus out there? This has been puzzling me for the longest, and whenever I come across any article about it, the answer shockingly is that physics has never really dealt with the question.
By velocity of gravity, I don't mean acceleration of an object being acted upon by gravity, but the speed of the propogation of gravity.
In other words, most physics models of bodies in space assume that, for example, the gravity of the sun acts instantaneously on the earth.
At the same time, relativity is supposed to limit all forces to the speed of light. In most scholarly articles, I understand the question, but the answers make my eyes glaze over. Here is an excerpt of a typical article that poses the question in an interesting way.
http://www.metaresearch.org/cosmology/speed_of_gravity.aspIntroduction
The most amazing thing I was taught as a graduate student of celestial mechanics at Yale in the 1960s was that all gravitational interactions between bodies in all dynamical systems had to be taken as instantaneous. This seemed unacceptable on two counts. In the first place, it seemed to be a form of "action at a distance". Perhaps no one has so elegantly expressed the objection to such a concept better than Sir Isaac Newton: "That one body may act upon another at a distance through a vacuum, without the mediation of any thing else, by and through which their action and force may be conveyed from one to the other, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it." (See Hoffman, 1983.) But mediation requires propagation, and finite bodies should be incapable of propagation at infinite speeds since that would require infinite energy. So instantaneous gravity seemed to have an element of magic to it.
The second objection was that we had all been taught that Einstein's special relativity (SR), an experimentally well established theory, proved that nothing could propagate in forward time at a speed greater than that of light in a vacuum. Indeed, as astronomers we were taught to calculate orbits using instantaneous forces; then extract the position of some body along its orbit at a time of interest, and calculate where that position would appear as seen from Earth by allowing for the finite propagation speed of light from there to here. It seemed incongruous to allow for the finite speed of light from the body to the Earth, but to take the effect of Earth's gravity on that same body as propagating from here to there instantaneously. Yet that was the required procedure to get the correct answers.
These objections were certainly not new when I raised them. They have been raised and answered thousands of times in dozens of different ways over the years since general relativity (GR) was set forth in 1916. Even today in discussions of gravity in USENET newsgroups on the Internet, the most frequently asked question and debated topic is "What is the speed of gravity?" It is only heard less often in the classroom because many teachers and most textbooks head off the question by hastily assuring students that gravitational waves propagate at the speed of light, leaving the firm impression, whether intended or not, that the question of gravity's propagation speed has already been answered.
Yet, anyone with a computer and orbit computation or numerical integration software can verify the consequences of introducing a delay into gravitational interactions. The effect on computed orbits is usually disastrous because conservation of angular momentum is destroyed. ...
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